Advanced Investment Science

Develops the mathematical foundations and computational methods for derivatives pricing and hedging, connecting classical financial theory with modern machine learning. Beginning with binomial models, replication, and risk-neutral valuation, the course progresses to Brownian motion, stochastic calculus, Itos lemma, and the Black-Scholes framework. These foundations support the study of implied volatility surfaces, option sensitivities, and dynamic hedging. The second half of the course then introduces generative adversarial networks (GANs) and diffusion models for generating implied volatility surfaces, with attention to market consistency and no-arbitrage constraints. It concludes with deep hedging, exploring how neural networks can learn hedging strategies under transaction costs and other market frictions. Throughout, the course emphasizes the connections among mathematical modeling, computational implementation, and financial risk management. Undergraduates need a permission code in order to enroll.